Attribute-Assisted Seismic Processing and Interpretation

http://geology.ou.edu/aaspi/

Joint seismic attributes visualization using Self-Organizing Maps

Marcílio Castro de Matos

marcilio@ou.edu

www.matos.eng.br

Kurt J. Marfurt

kmarfurt@ou.edu

Motivation: self organizing example

1- Choosing the attributes

Ex: The ratio between length and width

Bananas have high

ratio

Blueberries have ratio

close to one

L

W

L

W1

W

LPR 1

W

LPR

2- Clustering

Summary

• SOM review• SOM 1d• SOM 2d SOM 1d• SOM 2d colormap• SOM3d RGB

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xy

z

x y z

... ... ...

Winner prototype

vector

Training neighboohood

Input DATA MATRIX: 03 attributes with length 3000

13

7

91 (13x7) prototype vectors

Kohonen Self Organizing Maps

tmxthttmtm ibiii 1

ii

b mxmx min

e tbi

irbrth 2

2

2

Input Data: Cartesian coordinates of 3

gaussians centralized in [0,0,0] in red; [3,3,3] in

blue and [9,0,0] in green.The “+” signals represent

the vectors prototypes.

SOM map prototype vectors representation.

U-matrix

1 1-2 2 2-3 3 3-4 4

1-8 2-8 2-9 3-9 3-10 4-10 4-11

8 8-9 9 9-10 10 10-11 11

8-15 8-16 9-16 9-17 10-17 10-18 11-18

15 15-16 16 16-17 17 17-18 18

15-22 16-22 16-23 17-23 17-24 18-24 18-25

4-5 5 5-6 6 6-7 7

5-11 5-12 6-12 6-13 7-13 7-14

11-12 12 12-13 13 13-14 14

11-19 12-19 12-20 13-20 13-21 14-21

18-19 19 19-20 20 20-21 21

19-25 19-26 20-26 20-27 21-27 21-28

22 22-23 23 23-24 24 24-25 25

22-29 22-30 23-30 23-31 24-31 24-32 25-32

36 36-37 37 37-38 38 38-39 39

29 29-30 30 30-31 31 31-32 32

29-36 30-36 30-37 31-37 31-38 32-38 32-39

25-26 26 26-27 27 27-28 28

25-33 26-33 26-34 27-34 27-35 28-35

39-40 40 40-41 41 41-42 42

32-33 33 33-34 34 34-35 35

33-39 33-40 34-40 34-41 35-41 35-42

0.403

1.93

3.45U-matrix

…

Unified Distance Matrix (U-matrix) gives the distances between the neighboring map units.

Red color indicates long distances, and blue color indicates short distances.

This U-matrix representation gives an impression of “mountains” (long distances) which divide the map into “fields” (dense parts) or clusters.

Each cluster represents different classes.

0.403

1.93

3.45U-matrix

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xy

z

N samples (input data)

M prototype vectors

C classes

Abstraction level1 Abstraction level 22

Clustering of the SOM abstraction

>> >>

Kohonen Self Organizing Maps

Attr 2

Attr 1

Class1

Class3

Class2

Pre-image of prototypevectors from target space

1-D target space

2-D sourcespace

Kohonen Self Organizing Map

K-means clusters

K-means clustering tend to be attracted to the extreme values and are not ordered in a topological sequence.

(Coleou et al. 2003)

SOM-defined classes are in a sequence, so the process is less sensitive to the number of classes

Summary

• SOM review• SOM 1d• SOM 2d SOM 1d• SOM 2d colormap• SOM3d RGB

1D Self-Organizing Map12 classes

A color equidistant from each other has been got from the HSV circle and has been assigned to each class. It has not been taken into account the distance between the prototype vectors.

Classes

0°30°60°90°120°150°180°210°240°270°300°330°

1D Self-Organizing Map12 classes

Classes

HSV (Varying Hue, at fixed Saturation and Value) colormap

The distance among HSV color are proportional to the distance of the prototype vectors. This creates a smoother way to visually the classification result.

Classes

Taking into account the distance among

the prototype vectors

Principal component projection of the data

and the prototype vectors

Don’t taking into account the distance among the prototype

vectors

Classes

0°30°60°90°120°150°180°210°240°270°300°330°

1D Self-Organizing Map256 classes

Principal component projection of the data and the prototype vectors

Classes

Summary

• SOM review• SOM 1d• SOM 2d SOM 1d• SOM 2d colormap• SOM3d RGB

SOM 2D SOM 1D with 16 classes

Classes

2D SOM

+1D

SOM

1D SOM

Classes

Classes

SOM 2D SOM 1D with 256 classes

Classes

2D SOM colored prototype vectors and 1D SOM prototype vectors trajectory (white line)

Summary

• SOM review• SOM 1d• SOM 2d SOM 1d• SOM 2d colormap• SOM3d RGB

SOM 3D colormap

RGB cube

The RGB color model mapped to a cube. The horizontal x-axis as red values increasing to the left, y-axis as blue increasing to the lower right and the vertical z-axis as green increasing towards the top. The origin, black, is hidden behind the cube.

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position(1,i)

Neuron Positions

position(2,i)

positio

n(3

,i)

Acknowledgements

We also would like to thank PETROBRAS for their cooperation in providing the data, support and the authorization to publish this work.

Attribute-Assisted Seismic Processing and Interpretation

http://geology.ou.edu/aaspi/

The first two authors would like to thank the support from the University of Oklahoma Attribute-Assisted Seismic Processing and Interpretation Consortium and its sponsors.